Anovatech provides cloud computing services to other businesses. It uses

programmers (labor) and servers (capital) to produce its services. It costs

Anovatech $6,000 a month to hire a programmer, and $200 a month to rent

a server. (For simplicity, assume all inputs are continuously divisible.) Today,

Anovatech has 64 servers in their datacenters.

Anovatech can use servers to provide more service, or they can hire

programmers to think of ways to run those servers more eciently.

Anovatech's production function is proportional to the sum of the square

roots of the number of programmers they employ and the number of servers

they rent, so assume that q=K+L for some unit of output service.

1.In the short run, if Anovatech has a monthly budget of $200,000, what is the

highest production they can achieve?

2.Anovatech thinks they have an opportunity to win a contract for 30 units a

month of cloud computing service.

In the short run, what is the lowest cost at which Anovatech would be able to

produce 30 units a month of service?

(This cost may exceed their budget.)

Anovatech management thinks that cost is a bit steep in the short run, but

maybe in the long run they can bring the cost down.

3.In the long run, what is the lowest cost at which Anovatech would be able to

produce 30 units a month of service?

How many programmers and servers would they employ?

L=

K=

What percent cost savings does this represent, relative to the short term?

(Enter a positive number. You can enter an answer without the percent sign, like "0.4325", or with

it, like "43.25%", but

not

like "43.25".)